Related papers: Augmentation of Universal Potentials for Broad App…

We present a global optimizer, based on a conditional generative neural network, which can output ensembles of highly efficient topology-optimized metasurfaces operating across a range of parameters. A key feature of the network is that it…

Universal Machine Learning Interactomic Potentials (MLIPs) enable accelerated simulations for materials discovery. However, current research efforts fail to impactfully utilize MLIPs due to: 1. Overreliance on Density Functional Theory…

Finding the optimal configuration of parameters in ResNet is a nonconvex minimization problem, but first-order methods nevertheless find the global optimum in the overparameterized regime. We study this phenomenon with mean-field analysis,…

The lack of mathematical tractability of Deep Neural Networks (DNNs) has hindered progress towards having a unified convergence analysis of training algorithms, in the general setting. We propose a unified optimization framework for…

Modifications to a neural network's input and output layers are often required to accommodate the specificities of most practical learning tasks. However, the impact of such changes on architecture's approximation capabilities is largely…

Machine Learning techniques can be used to represent high-dimensional potential energy surfaces for reactive chemical systems. Two such methods are based on a reproducing kernel Hilbert space representation or on deep neural networks. They…

The properties of electrons in matter are of fundamental importance. They give rise to virtually all molecular and material properties and determine the physics at play in objects ranging from semiconductor devices to the interior of giant…

Phonons play a critical role in determining various material properties, but conventional methods for phonon calculations are computationally intensive, limiting their broad applicability. In this study, we present an approach to accelerate…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…

We derive a bound on the conformal dimensions of the lightest few states in general unitary 2d conformal field theories with discrete spectra using modular invariance, including CFTs with chiral currents. We derive a bound on the conformal…

Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…

One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory…

These days, although deep neural networks (DNNs) have achieved a noticeable progress in a wide range of research area, it lacks the adaptability to be employed in the real-world applications because of the environment discrepancy problem.…

Deep learning architectures are highly diverse. To prove their universal approximation properties, existing works typically rely on model-specific proofs. Generally, they construct a dedicated mathematical formulation for each architecture…

Nowadays, Computational Fluid Dynamics (CFD) is a fundamental tool for industrial design. However, the computational cost of doing such simulations is expensive and can be detrimental for real-world use cases where many simulations are…

Machine learned interatomic potentials (MLIPs) are becoming a standard method for DFT-level accurate molecular dynamics simulation and large-scale studies of crystal energetics. Increasingly popular are universal pre-trained potentials,…

This work studies the global convergence and implicit bias of Gauss Newton's (GN) when optimizing over-parameterized one-hidden layer networks in the mean-field regime. We first establish a global convergence result for GN in the…

Machine-learning interatomic potentials have emerged as a revolutionary class of force-field models in molecular simulations, delivering quantum-mechanical accuracy at a fraction of the computational cost and enabling the simulation of…

Recent developments in the field of deep learning for 3D data have demonstrated promising potential for end-to-end learning directly from point clouds. However, many real-world point clouds contain a large class im-balance due to the…

Binary metal clusters are of high interest for applications in heterogeneous catalysis and have received much attention in recent years. To gain insights into their structure and composition at the atomic scale, computer simulations can…